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Brochure 2016–2017 Edition

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Brochure 2016–2017 Edition CONTENTS Message from the Dean ……………………………………………………………………………………………… 1 Introduction of Teaching Faculty …………………………………………………………………………………… 2 Message from our Teaching Faculty ………………………………………………………………………………… 9 Education Programs : Original Program Fostering Creativity in Mathematics ……………………………… 10 Education Programs : Undergraduate Program …………………………………………………………… 12 Education Programs : Graduate Program for Master’s Degree ………………………………………………… 14 Education Programs : Graduate Program for Doctoral Degree (Ph. D.) …………………………………… 16 Tuition and Other Information ……………………………………………………………………………………… 18 International Activities …………………………………………………………………………………………… 20 Support for Education and Research …………………………………………………………………………… 24 The Cover Page: Ford Circles near √2 Ford circles let us visually understand the world of rational p 1 numbers. A Ford circle is a circle centered at ( q , 2q 2 ) with 1 p radius 2q 2 , where q is an irreducible fraction. Each Ford circle is tangent to the horizontal axis, and no two circles intersect with each other. In fact, one can fit all Ford circles beautifully in the upper half plane. The cover page shows the Ford circles corresponding to those rational numbers near √2. In particular, the bolder colored circles represent the first few 1 3 1 7 terms of the sequence 1, 1 + = 2 , 1 + 1 = , 2 2＋ 2 5 1 17 1 + 1 = , . , which converges to √2, as the following 2＋ 1 12 2＋ 2 continued fraction expansion of √2 shows: √2 = 1＋ 1 2＋ 1 2 1 ＋ 2 ＋… The figure suggests how quickly this sequence converges to √2. As this example shows, with the aid of Ford circles, theories involving rational numbers and continued fractions can be understood from a geometric aspect. Message from Dean Graduate School of Mathematics NAGOYA UNIVERSITY Enjoy your journey into mathematics! To those who take up this brochure Study and research in mathematics are often compared to mountain climbing. This is because the experience of piling up Dean of Graduate School of Mathematics logical steps to reach our goals or of obtaining surprising new prospects by finding unknown routes, viewpoints and concepts is Hiroaki Kanno similar to the experience of mountain climbing. The mathematics you have learned in high school and undergraduate programs is like climbing well-known mountains with a passage leading up to the start point of a mountain trail and a nicely paved path. But, in a graduate program, you often face punishing paths and untrampled routes. I do not necessarily mean forbidding lofty mountains such as the Himalayas. Even in familiar mountains nearby, there might be secret routes and hidden lookout points. It is also appealing to aim at mountains spreading over from mathematics to other academic fields. In recent years, many mountains crossing over the boundaries of mathematics have been discovered, ever expanding the research field of mathematics. If you are considering studying and researching mathematics in graduate school, please contemplate which mountain you would like to climb. I hope that the information on our faculty members and the mind map provided in this brochure will assist you in doing this. In mountain climbing, the higher your goals are, the greater the need is to develop physical strength and to gather background information. Even if you are planning to climb a familiar mountain, to avoid accidents, it is always important to check the weather forecast and to make prudent judgments. Just as in mountain climbing, learning and researching mathematics require considerable preparation and determination. As this brochure carefully explains, it is our belief that our graduate program provides sufficient support systems for you to study and research mathematics. Our basic policy in educational programs stresses fundamental knowledge of mathematics and broad coverage of various fields of it. Based upon this policy, we offer systematically organized courses, a wide variety of intensive courses, and a tutorial program under the supervision of advisors. We are also proud of our excellent library, secure computer network system, and friendly supporting staff. Furthermore, in recent years, we have been strengthening our career planning support. Perhaps some of you might think that you can do mathematics alone. But, to avoid becoming complacent, you should not neglect communicating with various people. I advise you to keep your intellectual curiosity, to ask questions when you are puzzled, and to try to explain to others when you discover something or solve interesting problems. These days, gathering information has become simple due to the development of the Internet. Yet, it cannot replace face-to-face communication with people from other academic disciplines or from different cultural backgrounds. We provide various opportunities for interaction such as Café David* and many events for international students. I encourage you to seize these opportunities. One of the biggest goals for a graduate student in mathematics is to submit a masters’ thesis or a doctoral thesis and have it approved by the thesis committee. It can be compared to writing a useful guidebook on a mountain you have investigated and making people interested in that mountain. I would like to invite you to find your favorite mountain and tell others its charm. We, the members of the Graduate School of Mathematics, will gladly help you in that endeavor. footnote *) a common office hour in our graduate school (see page 9). 1 Introduction of Teaching Faculty Keyword Keyword Integrable models, Conformal Programming languages, Type field theory theory My current subject is quantum field I am studying the theory underlying theory with infinite-dimensional functional programming languages. symmetry such as Virasoro algebra, For more than 15 years, I have for example, the string theory, been working at fitting types onto conformal field theory and two- the world, but the job is far from dimensional integrable model. finished. AWATA, Hidetoshi GARRIGUE, Jacques Keyword Keyword Graph colorings and labelings, Representation theory, Algebraic Traversability in graph, group Connectivity in graph In the area of graph theory, my I am working to formulate research interests include studying "(unknown) invariant theory" graph structures through graph which should associate to infinite colorings / labelings and distances dimensional representations, mainly in graphs. One of my current topics using algebraic analysis, algebraic is to study traversability in graphs geometry, and representation theory. using various covering walks. FUJIE-OKAMOTO, Futaba GYOJA, Akihiko Keyword Keyword Number theory, Arithmetic Mathematical physics, geometry, Non-commutative Elementary particle physics, class field theory Noncommutative solitons I am trying to understand a I am interested in the mathematical very primitive but basic object, structure behind laws of nature, "integers," via modern aspects especially elementary particle such as automorphic forms and physics and string theory. Presently, Shimura varieties (non-commutative I study noncommutative solitons and class field theory). My approach integrable systems related to N=2 mainly uses algebraic and geometric string theory and twistor theory. methods,including cohomology theory. FUJIWARA, Kazuhiro HAMANAKA, Masashi Keyword Keyword Number theory, Arithmetic Quantum information, geometry, Motivic fundamental Information theory groups I am working on (p-adic) periods In order to unravel the mystery of and (p-adic) differential equations quantum theory, I study quantum associated with motivic fundamental information theory based on the groups. I am also working on information theoretical aspect. My study structures of special types of treats this topic from the viewpoints of quantum groups associated with the information theory and representation KZ-equations. theory. FURUSHO, Hidekazu HAYASHI, Masahito 2 Graduate School of Mathematics NAGOYA UNIVERSITY Keyword Keyword Quantum group, Hopf algebra, Homogeneous spaces, Unitary Tensor category representations The field I am working in is quantum I study geometry and analysis on a groups and their representations. manifold whose symmetry is not so In particular, I am interested in small but not so large. I am interested generalized quantum groups and in how a 'strain' of the manifold is their relations to other areas of reflected on function spaces over the mathematics, such as classical manifold. representation theory and integrable systems. HAYASHI, Takahiro ISHI, Hideyuki Keyword Keyword Homotopy theory, Algebraic Hyperbolic geometry, Kleinian K-theory, p-adic arithmetic groups geometry My research focuses on the study of My research interest is the theory automorphisms of high dimensional of Kleinian groups. In this area, manifolds through homotopy theory, hyperbolic geometry, Riemann algebraic K-theory, and topological surfaces and low-dimensional cyclic homology. In this investigation, topology are closely related to each invariants and constructions in p-adic other. I study the deformation spaces arithmetic geometry naturally appear. of Kleinian groups which have fractal boundaries. HESSELHOLT, Lars ITO, Kentaro Keyword Keyword Complex Geometry, Bergman Crepant resolution, Quotient kernel, Monge-Ampère equation singularity, McKay correspondence I'm currently interested in the I study quotient singularities of geometry of the space of Kähler finite groups. I am interested in the metrics and various algebraic geometric and algebraic structure stability conditions. Geometric of them and their
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